What is the value of $x$ for which $|3x+5|$ is not positive? Express your answer as a common fraction.
Explanation: The only way $|3x+5|$ is not positive is if it is 0.  We have $|3x+5| = 0$ if and only if $3x+5 = 0$.  Solving this equation gives $x = \boxed{-\frac{5}{3}}$.